Rotor blade for a ninth phase of a compressor

ABSTRACT

The invention relates to a blade ( 10 ) of a rotor of a ninth phase of a compressor, which can be defined by coordinates of a discreet combination of points, in a Cartesian reference system (X,Y,Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, said blade ( 10 ) having a profile which can be identified by means of a series of closed intersection curves between the profile itself and planes (X,Y) lying at distances (Z) from the central axis, said blade ( 10 ) also comprising a thickening ( 30 ), substantially parallel to a base portion ( 12 ) of the blade ( 10 ) itself, fixable to said rotor, said thickening ( 30 ) being substantially situated half-way up the blade ( 10 ) and being suitable for shifting the natural resonance frequencies of the blade ( 10 ) itself outside a functioning frequency range of said rotor.

BACKGROUND OF THE INVENTION

The present invention relates to a blade of a rotor of a ninth phase of a compressor.

DESCRIPTION

More specifically, the invention relates to a blade of a rotor having a high aerodynamic efficiency of a ninth phase of a compressor.

Compressors normally pressurize in their interior air removed from the outside.

The fluid penetrates the compressor through a series of inlet ducts.

In these channels, the gas has low pressure and low temperature characteristics, whereas as it passes through the compressor, the gas is compressed and its temperature increases.

In order to increase the efficiency, the compressor is normally divided into various phases, each of which has a rotor and a stator respectively equipped with a series of blades.

In recent years, technologically advanced compressors have been further improved, obtaining an increased improvement in efficiency, operating in particular on the aerodynamic conditions.

The geometric configuration of the blades in fact significantly influences the aerodynamic efficiency.

This depends on the fact that the geometric characteristics of the blade cause a distribution of the relative velocities in the fluid, consequently influencing the distribution of the limit layers along the walls and, ultimately, losses due to friction.

In particular, in the case of rotor blades of a ninth phase of a compressor an extremely high efficiency is required, at the same time maintaining an appropriate aerodynamic and mechanical load.

An objective of the present invention is to provide a blade of a rotor of a ninth phase of a compressor which avoids or in any case reduces resonance problems due to flexural vibrations which reduce the life of the component, and at the same time allow a high aerodynamic efficiency.

A further objective of the present invention is to provide a rotor of a ninth phase of a compressor which allows a high aerodynamic efficiency and at the same time allows a high reliability of the compressor to be obtained with a consequent increase in the power of the turbine itself with the same compressor dimensions.

These objectives according to the present invention are achieved by providing a rotor blade of a ninth phase of a compressor as specified in claim 1.

Further characteristics of the invention are indicated in the subsequent claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The characteristics and advantages of a rotor blade of a ninth phase of a compressor according to the present invention will appear more evident from the following illustrative and non-limiting description, referring to the enclosed schematic drawings in which:

FIG. 1 is a raised view of a rotor blade of a compressor produced with an aerodynamic profile according to the present invention;

FIG. 2 is a raised view of the opposite side of the blade of FIG. 1; and

FIG. 3 is a diagram of the maximum thickness trend of a blade according to the present invention, with respect to its height.

With reference to the figures, a blade 10 is provided of a rotor of a ninth phase of a compressor.

Said blade 10 is defined by means of coordinates of a discreet combination of points, in a Cartesian reference system (X,Y,Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, not shown.

The profile of the blade 10 is identified by means of a series of closed intersection curves between the profile itself and planes (X,Y) lying at distances (Z) from the central axis.

The profile of said blade 10 comprises a first substantially concave surface 3, which is pressurized, and a second substantially convex surface 5 which is in depression and opposite the first.

The two surfaces 3, 5 are continuous and joined to each other, and together form the profile of said blade 10.

At a base portion 12, commonly called “foot” of the blade 10, according to the known art there is a connecting joint with the aerodynamic profile of the blade 10 itself, said base portion 12 being suitable for being fixed to said rotor of said compressor.

Said blade 10 comprises a thickening 30, i.e. a prolonged portion having a greater thickness with respect to the adjacent portions, which is substantially parallel to said base portion 12 so as to shift the resonance frequencies of said blade 10 outside a functioning frequency range of the rotor itself, thus reducing or in any case avoiding problems of instability and vibrations of the blade 10 and rotor.

This advantageously leads to an increase in both the useful life and reliability of the rotor and compressor itself.

Said thickening 30 relates to at least one section or closed curve, and is also situated half-way up the blade 10.

In other words, said thickening 30 confers a dynamic behaviour to said blade which is such as to have flexural frequencies which fall outside a functioning velocity range of the rotor of said compressor and consequently such that there is no intensification of the maximum flexural deformation of the blade during the functioning of the compressor.

This consequently leads to a higher performance of the compressor, of the rotor and a longer useful life of its components, as problems of resonance such as those described above are avoided.

The clearances and tolerances of the blade and stator can therefore be dimensioned so as to further increase the performances of the compressor itself.

This is possible as the blade 10 is prevented, upon deforming, from causing a contact and relative friction against the relative stator.

In particular, each closed curve has a maximum thickness determined by the maximum distance between said first surface 3 and said second surface 5.

Said maximum surface of each closed curve, along the height of the blade 10, moving towards a free end 14 of the blade 10, has first a decreasing and then an increasing trend, followed again by a decreasing and finally increasing trend, with two different slopes, said blade 10 comprising a further thickening substantially parallel to said base portion 12 and situated in particular close to said free end 14.

For example, the variation in the trend of the maximum thickness is shown in FIG. 3, in which it is compared with the maximum thickness trend of a blade according to the known art. In particular, in FIG. 3, the abscissa indicates the height of the blade 10, whereas the ordinate represents the maximum thickness of the blade 10, adimensionalized by putting the thickness in correspondence with the foot of the blade equal to 1. In the diagram shown in FIG. 3, the lower line represents the maximum thickness trend of a blade according to the known art, whereas the upper line shows the trend of the maximum thickness of the blade according to the present invention.

Along the height of the blade 10 in the direction of a free end 14 of the blade 10, said maximum thickness preferably has a trend which can be described by four different mathematical functions, identifying four different regions of the blade.

In the first region, that closest to the blade 10, up to a height equal to 45% of the height of the blade, the maximum thickness trend can be described by a polynomial function of the fourth degree (first decreasing and subsequently increasing) and in particular said polynomial function is:

Tmax=−34.522*h ⁴+36.4*h ³−8.4113*h ²−0.7259*h+0.9961

-   -   wherein h represents the percentage of the height of the blade         10, and wherein Tmax is the maximum adimensionalized thickness         relating to that closed curve corresponding to that percentage         of the height of the blade 10.

In the subsequent region, ranging from 45% to 58% of the height of the blade 10, the thickness varies according to the linear function (decreasing):

Tmax=−1.3509*h+1.4459

Therefore, between 58% and 86% of the height of the blade 10, the thickness trend is represented by the linear function (increasing):

Tmax=0.2074*h+0.5443

Finally, between 86% and the free end 14 of the blade, the maximum thickness varies according to the linear function (increasing):

Tmax=0.9058*h−0.0518

The profile of each blade 10 was also suitably shaped to be able to maintain the same efficiency at high levels.

The aerodynamic profile of each blade 10 is preferably defined by means of a series of closed curves whose coordinates are defined with respect to a Cartesian reference system X, Y, Z, wherein the axis Z is a radial axis intersecting the central axis of the turbine, and said closed curves lying at distances Z from the central axis are defined according to Table I, whose values, expressed in millimeters, refer to an aerodynamic profile at room temperature, in particular 25° C.

TABLE 1 X Y Z −8.852 9.902 255.999 −8.847 9.904 255.999 −8.835 9.905 255.999 −8.812 9.901 255.999 −8.771 9.880 255.999 −8.717 9.833 255.999 −8.632 9.734 255.999 −8.533 9.594 255.999 −8.410 9.400 255.999 −8.263 9.152 255.999 −8.080 8.826 255.999 −7.871 8.449 255.999 −7.643 8.050 255.999 −7.382 7.603 255.999 −7.086 7.110 255.999 −6.751 6.573 255.999 −6.390 6.019 255.999 −6.005 5.448 255.999 −5.593 4.860 255.999 −5.155 4.256 255.999 −4.688 3.638 255.999 −4.190 3.006 255.999 −3.660 2.364 255.999 −3.096 1.711 255.999 −2.520 1.069 255.999 −1.933 0.30278 255.999 −1.338 −0.189 255.999 −0.735 −0.806 255.999 −0.126 −1.417 255.999 0.33958 −2.023 255.999 1.108 −2.624 255.999 1.732 −3.219 255.999 2.362 −3.809 255.999 2.995 −4.395 255.999 3.631 −4.978 255.999 4.249 −5.538 255.999 4.849 −6.075 255.999 5.432 −6.588 255.999 5.998 −7.077 255.999 6.545 −7.543 255.999 7.075 −7.986 255.999 7.586 −8.405 255.999 8.056 −8.784 255.999 8.485 −9.124 255.999 8.871 −9.424 255.999 9.214 −9.685 255.999 9.515 −9.908 255.999 9.771 −10.093 255.999 9.992 −10.249 255.999 10.179 −10.379 255.999 10.332 −10.485 255.999 10.426 −10.600 255.999 10.461 −10.708 255.999 10.465 −10.793 255.999 10.452 −10.864 255.999 10.432 −10.917 255.999 10.411 −10.955 255.999 10.385 −10.991 255.999 10.343 −11.034 255.999 10.282 −11.077 255.999 10.199 −11.110 255.999 10.081 −11.119 255.999 9.933 −11.073 255.999 9.765 −10.976 255.999 9.561 −10.857 255.999 9.318 −10.717 255.999 9.034 −10.552 255.999 8.697 −10.359 255.999 8.308 −10.137 255.999 7.867 −9.884 255.999 7.376 −9.600 255.999 6.835 −9.282 255.999 6.245 −8.931 255.999 5.633 −8.559 255.999 4.999 −8.165 255.999 4.344 −7.748 255.999 3.670 −7.305 255.999 2.977 −6.837 255.999 2.267 −6.341 255.999 1.543 −5.816 255.999 0.57639 −5.280 255.999 0.08958 −4.730 255.999 −0.558 −4.165 255.999 −1.230 −3.583 255.999 −1.886 −2.983 255.999 −2.526 −2.366 255.999 −3.146 −1.727 255.999 −3.744 −1.064 255.999 −4.317 −0.373 255.999 −4.864 0.24028 255.999 −5.383 1.085 255.999 −5.861 1.816 255.999 −6.301 2.535 255.999 −6.704 3.242 255.999 −7.070 3.934 255.999 −7.401 4.611 255.999 −7.697 5.271 255.999 −7.962 5.912 255.999 −8.194 6.533 255.999 −8.387 7.104 255.999 −8.547 7.623 255.999 −8.675 8.088 255.999 −8.783 8.528 255.999 −8.864 8.911 255.999 −8.914 9.209 255.999 −8.940 9.449 255.999 −8.945 9.630 255.999 −8.932 9.765 255.999 −8.911 9.837 255.999 −8.887 9.878 255.999 −8.869 9.894 255.999 −8.858 9.900 255.999 −8.675 9.767 258.001 −8.669 9.769 258.001 −8.658 9.770 258.001 −8.635 9.767 258.001 −8.593 9.746 258.001 −8.538 9.700 258.001 −8.452 9.604 258.001 −8.349 9.465 258.001 −8.222 9.274 258.001 −8.069 9.031 258.001 −7.877 8.711 258.001 −7.657 8.340 258.001 −7.419 7.947 258.001 −7.147 7.508 258.001 −6.840 7.022 258.001 −6.494 6.493 258.001 −6.123 5.948 258.001 −5.726 5.385 258.001 −5.304 4.805 258.001 −4.855 4.211 258.001 −4.377 3.601 258.001 −3.871 2.978 258.001 −3.333 2.342 258.001 −2.766 1.694 258.001 −2.187 1.055 258.001 −1.600 0.29514 258.001 −1.004 −0.198 258.001 −0.402 −0.814 258.001 0.14236 −1.425 258.001 0.56736 −2.031 258.001 1.433 −2.634 258.001 2.053 −3.232 258.001 2.677 −3.827 258.001 3.304 −4.418 258.001 3.933 −5.006 258.001 4.545 −5.571 258.001 5.139 −6.113 258.001 5.715 −6.632 258.001 6.274 −7.127 258.001 6.815 −7.600 258.001 7.337 −8.049 258.001 7.841 −8.476 258.001 8.305 −8.861 258.001 8.728 −9.206 258.001 9.109 −9.512 258.001 9.448 −9.778 258.001 9.744 −10.005 258.001 9.997 −10.194 258.001 10.215 −10.354 258.001 10.399 −10.486 258.001 10.552 −10.594 258.001 10.671 −10.684 258.001 10.731 −10.780 258.001 10.749 −10.863 258.001 10.744 −10.934 258.001 10.727 −10.988 258.001 10.707 −11.026 258.001 10.680 −11.062 258.001 10.636 −11.102 258.001 10.570 −11.137 258.001 10.482 −11.152 258.001 10.366 −11.127 258.001 10.233 −11.049 258.001 10.067 −10.949 258.001 9.866 −10.828 258.001 9.626 −10.684 258.001 9.346 −10.517 258.001 9.013 −10.321 258.001 8.629 −10.094 258.001 8.194 −9.837 258.001 7.710 −9.547 258.001 7.176 −9.224 258.001 6.594 −8.867 258.001 5.990 −8.489 258.001 5.364 −8.089 258.001 4.718 −7.666 258.001 4.052 −7.219 258.001 3.368 −6.746 258.001 2.667 −6.245 258.001 1.952 −5.716 258.001 1.247 −5.175 258.001 0.38472 −4.623 258.001 −0.127 −4.057 258.001 −0.794 −3.477 258.001 −1.448 −2.882 258.001 −2.087 −2.272 258.001 −2.710 −1.644 258.001 −3.314 −0.995 258.001 −3.895 −0.323 258.001 −4.454 0.25903 258.001 −4.991 1.094 258.001 −5.485 1.807 258.001 −5.940 2.511 258.001 −6.356 3.203 258.001 −6.736 3.884 258.001 −7.080 4.549 258.001 −7.389 5.198 258.001 −7.668 5.828 258.001 −7.915 6.439 258.001 −8.123 7.002 258.001 −8.297 7.513 258.001 −8.438 7.971 258.001 −8.559 8.404 258.001 −8.653 8.782 258.001 −8.713 9.076 258.001 −8.746 9.313 258.001 −8.757 9.493 258.001 −8.749 9.627 258.001 −8.731 9.700 258.001 −8.708 9.742 258.001 −8.691 9.759 258.001 −8.680 9.765 258.001 −8.508 9.651 259.194 −8.503 9.652 259.194 −8.491 9.654 259.194 −8.468 9.651 259.194 −8.427 9.631 259.194 −8.371 9.586 259.194 −8.283 9.491 259.194 −8.177 9.355 259.194 −8.046 9.168 259.194 −7.887 8.929 259.194 −7.688 8.614 259.194 −7.459 8.249 259.194 −7.212 7.863 259.194 −6.931 7.429 259.194 −6.615 6.950 259.194 −6.261 6.428 259.194 −5.882 5.888 259.194 −5.480 5.331 259.194 −5.052 4.757 259.194 −4.598 4.166 259.194 −4.117 3.561 259.194 −3.607 2.941 259.194 −3.069 2.307 259.194 −2.502 1.660 259.194 −1.925 1.022 259.194 −1.339 0.27222 259.194 −0.745 −0.231 259.194 −0.144 −0.847 259.194 0.32083 −1.458 259.194 1.073 −2.064 259.194 1.687 −2.667 259.194 2.304 −3.266 259.194 2.925 −3.862 259.194 3.549 −4.454 259.194 4.175 −5.044 259.194 4.784 −5.611 259.194 5.374 −6.155 259.194 5.946 −6.677 259.194 6.501 −7.176 259.194 7.037 −7.652 259.194 7.555 −8.105 259.194 8.055 −8.535 259.194 8.515 −8.924 259.194 8.933 −9.273 259.194 9.311 −9.582 259.194 9.646 −9.851 259.194 9.940 −10.081 259.194 10.190 −10.273 259.194 10.406 −10.435 259.194 10.588 −10.570 259.194 10.739 −10.679 259.194 10.860 −10.766 259.194 10.943 −10.845 259.194 10.975 −10.924 259.194 10.978 −10.996 259.194 10.963 −11.052 259.194 10.943 −11.090 259.194 10.915 −11.125 259.194 10.868 −11.161 259.194 10.798 −11.187 259.194 10.709 −11.185 259.194 10.603 −11.133 259.194 10.472 −11.052 259.194 10.309 −10.951 259.194 10.110 −10.828 259.194 9.873 −10.683 259.194 9.595 −10.513 259.194 9.266 −10.314 259.194 8.886 −10.085 259.194 8.456 −9.824 259.194 7.977 −9.531 259.194 7.449 −9.204 259.194 6.873 −8.842 259.194 6.275 −8.460 259.194 5.655 −8.057 259.194 5.015 −7.630 259.194 4.355 −7.180 259.194 3.678 −6.705 259.194 2.985 −6.205 259.194 2.278 −5.676 259.194 1.581 −5.137 259.194 0.62222 −4.586 259.194 0.15417 −4.023 259.194 −0.440 −3.446 259.194 −1.088 −2.855 259.194 −1.722 −2.249 259.194 −2.340 −1.626 259.194 −2.941 −0.984 259.194 −3.522 −0.322 259.194 −4.082 0.25139 259.194 −4.622 1.069 259.194 −5.124 1.773 259.194 −5.588 2.470 259.194 −6.014 3.155 259.194 −6.405 3.828 259.194 −6.760 4.486 259.194 −7.084 5.127 259.194 −7.377 5.750 259.194 −7.640 6.353 259.194 −7.864 6.909 259.194 −8.053 7.413 259.194 −8.209 7.866 259.194 −8.345 8.294 259.194 −8.451 8.668 259.194 −8.521 8.959 259.194 −8.563 9.195 259.194 −8.580 9.374 259.194 −8.577 9.509 259.194 −8.562 9.582 259.194 −8.540 9.625 259.194 −8.524 9.642 259.194 −8.514 9.648 259.194 −8.337 9.565 260.388 −8.331 9.567 260.388 −8.320 9.569 260.388 −8.297 9.566 260.388 −8.255 9.547 260.388 −8.198 9.503 260.388 −8.109 9.409 260.388 −8.001 9.275 260.388 −7.867 9.090 260.388 −7.705 8.854 260.388 −7.499 8.543 260.388 −7.264 8.183 260.388 −7.010 7.801 260.388 −6.723 7.373 260.388 −6.401 6.899 260.388 −6.041 6.381 260.388 −5.658 5.845 260.388 −5.252 5.291 260.388 −4.820 4.720 260.388 −4.364 4.133 260.388 −3.880 3.529 260.388 −3.370 2.911 260.388 −2.831 2.278 260.388 −2.265 1.632 260.388 −1.689 0.69028 260.388 −1.105 0.25278 260.388 −0.514 −0.259 260.388 0.084 −0.876 260.388 0.47708 −1.489 260.388 1.294 −2.096 260.388 1.906 −2.701 260.388 2.520 −3.301 260.388 3.139 −3.898 260.388 3.760 −4.492 260.388 4.384 −5.083 260.388 4.990 −5.651 260.388 5.578 −6.197 260.388 6.147 −6.720 260.388 6.699 −7.221 260.388 7.232 −7.699 260.388 7.747 −8.154 260.388 8.245 −8.586 260.388 8.702 −8.977 260.388 9.118 −9.328 260.388 9.494 −9.638 260.388 9.827 −9.909 260.388 10.119 −10.141 260.388 10.367 −10.335 260.388 10.581 −10.498 260.388 10.762 −10.634 260.388 10.912 −10.745 260.388 11.032 −10.833 260.388 11.118 −10.909 260.388 11.153 −10.987 260.388 11.157 −11.059 260.388 11.142 −11.115 260.388 11.122 −11.153 260.388 11.093 −11.187 260.388 11.045 −11.222 260.388 10.975 −11.244 260.388 10.887 −11.238 260.388 10.783 −11.182 260.388 10.654 −11.099 260.388 10.493 −10.996 260.388 10.297 −10.871 260.388 10.063 −10.723 260.388 9.789 −10.550 260.388 9.465 −10.347 260.388 9.090 −10.114 260.388 8.666 −9.848 260.388 8.193 −9.549 260.388 7.672 −9.216 260.388 7.104 −8.848 260.388 6.514 −8.460 260.388 5.902 −8.050 260.388 5.270 −7.617 260.388 4.619 −7.162 260.388 3.950 −6.683 260.388 3.265 −6.178 260.388 2.564 −5.646 260.388 1.874 −5.104 260.388 1.194 −4.550 260.388 0.36458 −3.983 260.388 −0.132 −3.404 260.388 −0.777 −2.810 260.388 −1.407 −2.202 260.388 −2.024 −1.577 260.388 −2.624 −0.935 260.388 −3.206 −0.273 260.388 −3.769 0.28472 260.388 −4.313 1.114 260.388 −4.818 1.811 260.388 −5.284 2.498 260.388 −5.714 3.173 260.388 −6.111 3.836 260.388 −6.474 4.483 260.388 −6.805 5.113 260.388 −7.109 5.725 260.388 −7.383 6.318 260.388 −7.619 6.863 260.388 −7.819 7.359 260.388 −7.987 7.803 260.388 −8.133 8.224 260.388 −8.249 8.592 260.388 −8.327 8.879 260.388 −8.376 9.111 260.388 −8.398 9.288 260.388 −8.399 9.422 260.388 −8.387 9.495 260.388 −8.368 9.538 260.388 −8.352 9.556 260.388 −8.342 9.562 260.388 −8.170 9.508 261.582 −8.164 9.510 261.582 −8.153 9.512 261.582 −8.130 9.509 261.582 −8.088 9.490 261.582 −8.031 9.446 261.582 −7.941 9.354 261.582 −7.832 9.222 261.582 −7.695 9.038 261.582 −7.530 8.804 261.582 −7.321 8.496 261.582 −7.081 8.140 261.582 −6.823 7.761 261.582 −6.531 7.336 261.582 −6.205 6.866 261.582 −5.841 6.352 261.582 −5.454 5.819 261.582 −5.045 5.268 261.582 −4.611 4.700 261.582 −4.152 4.114 261.582 −3.668 3.512 261.582 −3.156 2.895 261.582 −2.618 2.263 261.582 −2.052 1.618 261.582 −1.478 0.68056 261.582 −0.896 0.24236 261.582 −0.307 −0.277 261.582 0.19931 −0.896 261.582 0.61597 −1.511 261.582 1.491 −2.122 261.582 2.099 −2.728 261.582 2.711 −3.330 261.582 3.327 −3.929 261.582 3.945 −4.525 261.582 4.566 −5.118 261.582 5.170 −5.688 261.582 5.755 −6.235 261.582 6.322 −6.760 261.582 6.871 −7.263 261.582 7.402 −7.742 261.582 7.915 −8.199 261.582 8.410 −8.633 261.582 8.865 −9.026 261.582 9.280 −9.378 261.582 9.653 −9.690 261.582 9.985 −9.963 261.582 10.275 −10.196 261.582 10.522 −10.391 261.582 10.735 −10.556 261.582 10.915 −10.693 261.582 11.064 −10.805 261.582 11.183 −10.894 261.582 11.268 −10.970 261.582 11.303 −11.048 261.582 11.306 −11.119 261.582 11.291 −11.174 261.582 11.271 −11.212 261.582 11.242 −11.246 261.582 11.193 −11.280 261.582 11.123 −11.301 261.582 11.035 −11.292 261.582 10.933 −11.234 261.582 10.806 −11.150 261.582 10.646 −11.046 261.582 10.453 −10.919 261.582 10.222 −10.768 261.582 9.951 −10.592 261.582 9.630 −10.386 261.582 9.260 −10.147 261.582 8.841 −9.876 261.582 8.375 −9.572 261.582 7.860 −9.233 261.582 7.299 −8.858 261.582 6.716 −8.463 261.582 6.112 −8.047 261.582 5.488 −7.608 261.582 4.845 −7.147 261.582 4.184 −6.661 261.582 3.507 −6.151 261.582 2.814 −5.614 261.582 2.130 −5.068 261.582 1.457 −4.510 261.582 0.55139 −3.942 261.582 0.09931 −3.360 261.582 −0.496 −2.764 261.582 −1.121 −2.154 261.582 −1.733 −1.529 261.582 −2.329 −0.888 261.582 −2.909 −0.229 261.582 −3.471 0.31181 261.582 −4.016 1.147 261.582 −4.523 1.839 261.582 −4.993 2.519 261.582 −5.429 3.188 261.582 −5.831 3.843 261.582 −6.202 4.483 261.582 −6.543 5.106 261.582 −6.855 5.710 261.582 −7.140 6.295 261.582 −7.386 6.833 261.582 −7.597 7.322 261.582 −7.773 7.762 261.582 −7.929 8.177 261.582 −8.054 8.541 261.582 −8.139 8.824 261.582 −8.194 9.055 261.582 −8.222 9.230 261.582 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263.972 −1.787 1.599 263.972 −1.216 0.66597 263.972 −0.640 0.225 263.972 −0.058 −0.306 263.972 0.36736 −0.931 263.972 1.122 −1.551 263.972 1.719 −2.166 263.972 2.320 −2.778 263.972 2.926 −3.385 263.972 3.535 −3.989 263.972 4.147 −4.590 263.972 4.762 −5.188 263.972 5.359 −5.762 263.972 5.939 −6.314 263.972 6.501 −6.843 263.972 7.046 −7.350 263.972 7.572 −7.833 263.972 8.081 −8.294 263.972 8.571 −8.732 263.972 9.022 −9.128 263.972 9.433 −9.484 263.972 9.802 −9.800 263.972 10.130 −10.076 263.972 10.417 −10.312 263.972 10.661 −10.510 263.972 10.872 −10.678 263.972 11.049 −10.818 263.972 11.196 −10.932 263.972 11.313 −11.023 263.972 11.398 −11.099 263.972 11.432 −11.178 263.972 11.434 −11.249 263.972 11.418 −11.304 263.972 11.396 −11.341 263.972 11.367 −11.374 263.972 11.318 −11.406 263.972 11.247 −11.426 263.972 11.160 −11.415 263.972 11.060 −11.355 263.972 10.936 −11.268 263.972 10.780 −11.160 263.972 10.591 −11.029 263.972 10.365 −10.873 263.972 10.101 −10.690 263.972 9.788 −10.476 263.972 9.427 −10.228 263.972 9.019 −9.947 263.972 8.564 −9.630 263.972 8.062 −9.278 263.972 7.515 −8.890 263.972 6.947 −8.480 263.972 6.358 −8.050 263.972 5.750 −7.596 263.972 5.123 −7.120 263.972 4.478 −6.621 263.972 3.817 −6.097 263.972 3.141 −5.547 263.972 2.473 −4.988 263.972 1.814 −4.421 263.972 1.165 −3.843 263.972 0.36597 −3.254 263.972 −0.099 −2.652 263.972 −0.712 −2.038 263.972 −1.313 −1.411 263.972 −1.901 −0.771 263.972 −2.475 −0.116 263.972 −3.032 0.38542 263.972 −3.574 1.242 263.972 −4.083 1.922 263.972 −4.560 2.592 263.972 −5.005 3.250 263.972 −5.418 3.893 263.972 −5.801 4.520 263.972 −6.155 5.130 263.972 −6.483 5.722 263.972 −6.784 6.295 263.972 −7.046 6.821 263.972 −7.273 7.299 263.972 −7.465 7.729 263.972 −7.636 8.135 263.972 −7.776 8.491 263.972 −7.873 8.769 263.972 −7.939 8.995 263.972 −7.976 9.167 263.972 −7.990 9.299 263.972 −7.985 9.372 263.972 −7.971 9.417 263.972 −7.958 9.436 263.972 −7.949 9.443 263.972 −7.918 9.437 264.569 −7.912 9.439 264.569 −7.901 9.441 264.569 −7.878 9.438 264.569 −7.836 9.419 264.569 −7.779 9.376 264.569 −7.688 9.284 264.569 −7.578 9.153 264.569 −7.440 8.971 264.569 −7.272 8.739 264.569 −7.058 8.435 264.569 −6.812 8.084 264.569 −6.549 7.710 264.569 −6.252 7.290 264.569 −5.920 6.824 264.569 −5.550 6.316 264.569 −5.158 5.787 264.569 −4.745 5.240 264.569 −4.308 4.675 264.569 −3.848 4.092 264.569 −3.363 3.492 264.569 −2.852 2.876 264.569 −2.316 2.244 264.569 −1.754 1.596 264.569 −1.185 0.66319 264.569 −0.610 0.22153 264.569 −0.029 −0.312 264.569 0.38611 −0.938 264.569 1.147 −1.560 264.569 1.743 −2.177 264.569 2.343 −2.790 264.569 2.946 −3.399 264.569 3.553 −4.005 264.569 4.164 −4.607 264.569 4.777 −5.207 264.569 5.373 −5.783 264.569 5.951 −6.336 264.569 6.511 −6.867 264.569 7.054 −7.375 264.569 7.579 −7.859 264.569 8.086 −8.322 264.569 8.575 −8.761 264.569 9.025 −9.159 264.569 9.434 −9.516 264.569 9.802 −9.833 264.569 10.129 −10.110 264.569 10.415 −10.348 264.569 10.659 −10.547 264.569 10.868 −10.716 264.569 11.045 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264.569 −5.741 4.531 264.569 −6.099 5.138 264.569 −6.429 5.727 264.569 −6.733 6.298 264.569 −6.998 6.822 264.569 −7.228 7.298 264.569 −7.423 7.725 264.569 −7.597 8.130 264.569 −7.740 8.484 264.569 −7.840 8.761 264.569 −7.908 8.985 264.569 −7.946 9.157 264.569 −7.961 9.289 264.569 −7.958 9.362 264.569 −7.945 9.407 264.569 −7.932 9.426 264.569 −7.923 9.434 264.569 −7.904 9.427 265.166 −7.898 9.430 265.166 −7.887 9.432 265.166 −7.864 9.429 265.166 −7.822 9.410 265.166 −7.765 9.367 265.166 −7.674 9.276 265.166 −7.563 9.144 265.166 −7.424 8.963 265.166 −7.256 8.732 265.166 −7.041 8.429 265.166 −6.795 8.078 265.166 −6.530 7.705 265.166 −6.232 7.285 265.166 −5.899 6.821 265.166 −5.528 6.313 265.166 −5.136 5.786 265.166 −4.721 5.240 265.166 −4.284 4.675 265.166 −3.823 4.093 265.166 −3.337 3.493 265.166 −2.827 2.877 265.166 −2.291 2.245 265.166 −1.730 1.597 265.166 −1.162 0.66319 265.166 −0.588 0.22083 265.166 −0.009 −0.315 265.166 0.39931 −0.942 265.166 1.164 −1.565 265.166 1.758 −2.183 265.166 2.356 −2.798 265.166 2.957 −3.410 265.166 3.561 −4.017 265.166 4.169 −4.622 265.166 4.780 −5.223 265.166 5.374 −5.801 265.166 5.950 −6.357 265.166 6.509 −6.889 265.166 7.050 −7.399 265.166 7.573 −7.886 265.166 8.078 −8.350 265.166 8.565 −8.791 265.166 9.013 −9.191 265.166 9.420 −9.550 265.166 9.787 −9.868 265.166 10.113 −10.147 265.166 10.397 −10.386 265.166 10.640 −10.586 265.166 10.848 −10.756 265.166 11.024 −10.897 265.166 11.170 −11.013 265.166 11.286 −11.105 265.166 11.369 −11.182 265.166 11.401 −11.261 265.166 11.402 −11.332 265.166 11.385 −11.386 265.166 11.363 −11.423 265.166 11.333 −11.455 265.166 11.284 −11.487 265.166 11.214 −11.506 265.166 11.127 −11.495 265.166 11.028 −11.434 265.166 10.905 −11.346 265.166 10.750 −11.236 265.166 10.563 −11.102 265.166 10.340 −10.944 265.166 10.078 −10.759 265.166 9.769 −10.540 265.166 9.412 −10.288 265.166 9.008 −10.002 265.166 8.558 −9.681 265.166 8.062 −9.323 265.166 7.521 −8.928 265.166 6.959 −8.512 265.166 6.377 −8.075 265.166 5.775 −7.615 265.166 5.155 −7.132 265.166 4.517 −6.626 265.166 3.863 −6.095 265.166 3.194 −5.538 265.166 2.534 −4.973 265.166 1.882 −4.400 265.166 1.240 −3.816 265.166 0.42222 −3.222 265.166 −0.011 −2.617 265.166 −0.620 −2.000 265.166 −1.216 −1.371 265.166 −1.800 −0.729 265.166 −2.369 −0.074 265.166 −2.924 0.41389 265.166 −3.464 1.281 265.166 −3.972 1.957 265.166 −4.450 2.622 265.166 −4.897 3.276 265.166 −5.313 3.915 265.166 −5.700 4.537 265.166 −6.060 5.143 265.166 −6.392 5.730 265.166 −6.699 6.298 265.166 −6.966 6.820 265.166 −7.199 7.294 265.166 −7.396 7.720 265.166 −7.572 8.123 265.166 −7.717 8.475 265.166 −7.819 8.750 265.166 −7.889 8.975 265.166 −7.929 9.147 265.166 −7.946 9.278 265.166 −7.943 9.352 265.166 −7.931 9.397 265.166 −7.918 9.417 265.166 −7.909 9.424 265.166 −7.900 9.417 265.763 −7.895 9.420 265.763 −7.884 9.422 265.763 −7.861 9.419 265.763 −7.819 9.400 265.763 −7.761 9.357 265.763 −7.669 9.267 265.763 −7.558 9.136 265.763 −7.419 8.956 265.763 −7.250 8.725 265.763 −7.034 8.423 265.763 −6.786 8.073 265.763 −6.521 7.701 265.763 −6.221 7.283 265.763 −5.887 6.820 265.763 −5.515 6.313 265.763 −5.121 5.787 265.763 −4.705 5.242 265.763 −4.267 4.678 265.763 −3.805 4.097 265.763 −3.319 3.498 265.763 −2.809 2.882 265.763 −2.274 2.250 265.763 −1.713 1.602 265.763 −1.146 0.66597 265.763 −0.574 0.22292 265.763 0.003 −0.312 265.763 0.40625 −0.941 265.763 1.172 −1.565 265.763 1.764 −2.186 265.763 2.359 −2.802 265.763 2.958 −3.416 265.763 3.560 −4.026 265.763 4.165 −4.633 265.763 4.773 −5.237 265.763 5.364 −5.817 265.763 5.938 −6.375 265.763 6.494 −6.909 265.763 7.032 −7.421 265.763 7.553 −7.910 265.763 8.055 −8.377 265.763 8.540 −8.820 265.763 8.985 −9.222 265.763 9.391 −9.583 265.763 9.756 −9.903 265.763 10.080 −10.184 265.763 10.363 −10.424 265.763 10.604 −10.626 265.763 10.812 −10.796 265.763 10.987 −10.939 265.763 11.132 −11.055 265.763 11.248 −11.148 265.763 11.332 −11.225 265.763 11.366 −11.305 265.763 11.367 −11.377 265.763 11.350 −11.433 265.763 11.328 −11.470 265.763 11.298 −11.503 265.763 11.249 −11.534 265.763 11.178 −11.553 265.763 11.091 −11.541 265.763 10.993 −11.480 265.763 10.870 −11.391 265.763 10.716 −11.281 265.763 10.530 −11.146 265.763 10.307 −10.986 265.763 10.047 −10.800 265.763 9.739 −10.580 265.763 9.383 −10.327 265.763 8.981 −10.038 265.763 8.533 −9.714 265.763 8.039 −9.354 265.763 7.500 −8.957 265.763 6.940 −8.538 265.763 6.361 −8.098 265.763 5.762 −7.635 265.763 5.144 −7.149 265.763 4.509 −6.640 265.763 3.858 −6.106 265.763 3.192 −5.547 265.763 2.535 −4.979 265.763 1.886 −4.402 265.763 1.247 −3.816 265.763 0.42986 −3.220 265.763 0.001 −2.612 265.763 −0.605 −1.994 265.763 −1.199 −1.364 265.763 −1.780 −0.721 265.763 −2.348 −0.065 265.763 −2.901 0.42014 265.763 −3.440 1.290 265.763 −3.947 1.965 265.763 −4.424 2.629 265.763 −4.872 3.281 265.763 −5.290 3.918 265.763 −5.678 4.539 265.763 −6.039 5.143 265.763 −6.374 5.729 265.763 −6.682 6.295 265.763 −6.951 6.816 265.763 −7.185 7.289 265.763 −7.385 7.714 265.763 −7.563 8.115 265.763 −7.709 8.467 265.763 −7.812 8.741 265.763 −7.883 8.965 265.763 −7.924 9.137 265.763 −7.941 9.268 265.763 −7.939 9.342 265.763 −7.927 9.387 265.763 −7.914 9.407 265.763 −7.905 9.414 265.763 −7.906 9.405 266.360 −7.901 9.408 266.360 −7.889 9.410 266.360 −7.866 9.408 266.360 −7.824 9.389 266.360 −7.766 9.347 266.360 −7.674 9.257 266.360 −7.562 9.127 266.360 −7.421 8.947 266.360 −7.251 8.718 266.360 −7.034 8.417 266.360 −6.785 8.068 266.360 −6.518 7.697 266.360 −6.217 7.280 266.360 −5.880 6.818 266.360 −5.507 6.313 266.360 −5.111 5.788 266.360 −4.694 5.244 266.360 −4.255 4.681 266.360 −3.792 4.101 266.360 −3.306 3.502 266.360 −2.795 2.887 266.360 −2.260 2.255 266.360 −1.699 1.606 266.360 −1.134 0.66806 266.360 −0.563 0.22431 266.360 0.012 −0.312 266.360 0.41181 −0.942 266.360 1.178 −1.568 266.360 1.768 −2.190 266.360 2.361 −2.809 266.360 2.956 −3.425 266.360 3.555 −4.038 266.360 4.158 −4.648 266.360 4.763 −5.254 266.360 5.351 −5.838 266.360 5.922 −6.398 266.360 6.475 −6.936 266.360 7.011 −7.450 266.360 7.529 −7.942 266.360 8.029 −8.411 266.360 8.511 −8.858 266.360 8.954 −9.262 266.360 9.357 −9.625 266.360 9.721 −9.948 266.360 10.043 −10.230 266.360 10.324 −10.473 266.360 10.564 −10.675 266.360 10.771 −10.847 266.360 10.945 −10.991 266.360 11.089 −11.108 266.360 11.205 −11.201 266.360 11.288 −11.279 266.360 11.321 −11.359 266.360 11.322 −11.431 266.360 11.305 −11.486 266.360 11.283 −11.524 266.360 11.252 −11.556 266.360 11.203 −11.588 266.360 11.133 −11.606 266.360 11.046 −11.594 266.360 10.947 −11.532 266.360 10.825 −11.443 266.360 10.672 −11.331 266.360 10.486 −11.196 266.360 10.265 −11.035 266.360 10.005 −10.848 266.360 9.698 −10.627 266.360 9.344 −10.371 266.360 8.943 −10.081 266.360 8.496 −9.755 266.360 8.004 −9.393 266.360 7.467 −8.993 266.360 6.909 −8.573 266.360 6.332 −8.130 266.360 5.735 −7.665 266.360 5.119 −7.176 266.360 4.487 −6.664 266.360 3.838 −6.128 266.360 3.175 −5.565 266.360 2.520 −4.995 266.360 1.874 −4.415 266.360 1.237 −3.827 266.360 0.42431 −3.228 266.360 −0.004 −2.618 266.360 −0.607 −1.998 266.360 −1.199 −1.366 266.360 −1.779 −0.722 266.360 −2.344 −0.065 266.360 −2.896 0.42083 266.360 −3.434 1.290 266.360 −3.940 1.964 266.360 −4.417 2.628 266.360 −4.864 3.279 266.360 −5.282 3.915 266.360 −5.672 4.535 266.360 −6.034 5.138 266.360 −6.370 5.723 266.360 −6.679 6.288 266.360 −6.950 6.808 266.360 −7.186 7.280 266.360 −7.386 7.704 266.360 −7.565 8.105 266.360 −7.712 8.456 266.360 −7.816 8.730 266.360 −7.888 8.954 266.360 −7.929 9.125 266.360 −7.947 9.256 266.360 −7.945 9.330 266.360 −7.933 9.375 266.360 −7.920 9.395 266.360 −7.911 9.402 266.360 −7.918 9.391 266.957 −7.913 9.393 266.957 −7.902 9.396 266.957 −7.878 9.394 266.957 −7.836 9.376 266.957 −7.778 9.334 266.957 −7.684 9.245 266.957 −7.571 9.116 266.957 −7.430 8.937 266.957 −7.258 8.709 266.957 −7.039 8.409 266.957 −6.788 8.062 266.957 −6.520 7.692 266.957 −6.217 7.276 266.957 −5.879 6.816 266.957 −5.503 6.312 266.957 −5.106 5.788 266.957 −4.688 5.245 266.957 −4.247 4.683 266.957 −3.783 4.104 266.957 −3.295 3.506 266.957 −2.784 2.891 266.957 −2.249 2.259 266.957 −1.689 1.610 266.957 −1.125 0.67014 266.957 −0.555 0.22569 266.957 0.019 −0.312 266.957 0.41528 −0.944 266.957 1.181 −1.572 266.957 1.768 −2.196 266.957 2.359 −2.818 266.957 2.951 −3.436 266.957 3.547 −4.052 266.957 4.147 −4.665 266.957 4.749 −5.275 266.957 5.334 −5.862 266.957 5.901 −6.425 266.957 6.451 −6.966 266.957 6.984 −7.484 266.957 7.499 −7.979 266.957 7.996 −8.451 266.957 8.475 −8.900 266.957 8.916 −9.308 266.957 9.317 −9.674 266.957 9.678 −9.999 266.957 9.998 −10.283 266.957 10.278 −10.527 266.957 10.517 −10.731 266.957 10.722 −10.905 266.957 10.896 −11.049 266.957 11.039 −11.167 266.957 11.154 −11.261 266.957 11.237 −11.339 266.957 11.270 −11.419 266.957 11.270 −11.492 266.957 11.253 −11.547 266.957 11.230 −11.585 266.957 11.200 −11.617 266.957 11.150 −11.648 266.957 11.080 −11.666 266.957 10.993 −11.654 266.957 10.895 −11.591 266.957 10.773 −11.501 266.957 10.620 −11.389 266.957 10.435 −11.253 266.957 10.214 −11.092 266.957 9.955 −10.903 266.957 9.649 −10.681 266.957 9.296 −10.424 266.957 8.896 −10.132 266.957 8.450 −9.805 266.957 7.959 −9.441 266.957 7.423 −9.039 266.957 6.867 −8.616 266.957 6.291 −8.172 266.957 5.696 −7.704 266.957 5.082 −7.213 266.957 4.451 −6.699 266.957 3.804 −6.160 266.957 3.143 −5.595 266.957 2.490 −5.021 266.957 1.846 −4.439 266.957 1.212 −3.848 266.957 0.40903 −3.247 266.957 −0.024 −2.636 266.957 −0.626 −2.013 266.957 −1.215 −1.380 266.957 −1.793 −0.734 266.957 −2.357 −0.076 266.957 −2.907 0.41389 266.957 −3.443 1.281 266.957 −3.948 1.955 266.957 −4.424 2.618 266.957 −4.871 3.268 266.957 −5.290 3.905 266.957 −5.680 4.524 266.957 −6.042 5.127 266.957 −6.379 5.711 266.957 −6.689 6.276 266.957 −6.961 6.795 266.957 −7.196 7.267 266.957 −7.397 7.690 266.957 −7.577 8.091 266.957 −7.725 8.442 266.957 −7.828 8.716 266.957 −7.900 8.939 266.957 −7.942 9.111 266.957 −7.960 9.242 266.957 −7.958 9.315 266.957 −7.945 9.361 266.957 −7.932 9.380 266.957 −7.923 9.388 266.957 −8.048 9.150 271.165 −8.043 9.153 271.165 −8.032 9.156 271.165 −8.008 9.157 271.165 −7.964 9.144 271.165 −7.902 9.108 271.165 −7.802 9.026 271.165 −7.682 8.903 271.165 −7.531 8.731 271.165 −7.350 8.510 271.165 −7.121 8.216 271.165 −6.859 7.876 271.165 −6.580 7.513 271.165 −6.267 7.103 271.165 −5.920 6.648 271.165 −5.535 6.150 271.165 −5.131 5.630 271.165 −4.706 5.090 271.165 −4.261 4.530 271.165 −3.794 3.950 271.165 −3.306 3.351 271.165 −2.796 2.733 271.165 −2.264 2.095 271.165 −1.710 1.439 271.165 −1.152 0.54583 271.165 −0.592 0.09375 271.165 −0.030 −0.515 271.165 0.37083 −1.162 271.165 1.101 −1.807 271.165 1.670 −2.450 271.165 2.240 −3.093 271.165 2.812 −3.733 271.165 3.385 −4.373 271.165 3.961 −5.010 271.165 4.539 −5.645 271.165 5.100 −6.257 271.165 5.644 −6.845 271.165 6.172 −7.410 271.165 6.683 −7.951 271.165 7.177 −8.469 271.165 7.654 −8.963 271.165 8.115 −9.433 271.165 8.539 −9.860 271.165 8.925 −10.243 271.165 9.274 −10.583 271.165 9.583 −10.880 271.165 9.854 −11.136 271.165 10.085 −11.349 271.165 10.284 −11.530 271.165 10.453 −11.681 271.165 10.592 −11.805 271.165 10.704 −11.903 271.165 10.784 −11.984 271.165 10.815 −12.066 271.165 10.813 −12.138 271.165 10.794 −12.193 271.165 10.770 −12.230 271.165 10.739 −12.261 271.165 10.689 −12.292 271.165 10.617 −12.308 271.165 10.531 −12.293 271.165 10.434 −12.227 271.165 10.314 −12.134 271.165 10.165 −12.018 271.165 9.982 −11.876 271.165 9.765 −11.709 271.165 9.510 −11.513 271.165 9.208 −11.283 271.165 8.860 −11.018 271.165 8.465 −10.717 271.165 8.025 −10.380 271.165 7.540 −10.004 271.165 7.012 −9.590 271.165 6.463 −9.155 271.165 5.894 −8.698 271.165 5.307 −8.217 271.165 4.702 −7.713 271.165 4.080 −7.184 271.165 3.443 −6.630 271.165 2.793 −6.049 271.165 2.151 −5.461 271.165 1.518 −4.864 271.165 0.62153 −4.258 271.165 0.19583 −3.642 271.165 −0.319 −3.016 271.165 −0.909 −2.380 271.165 −1.488 −1.733 271.165 −2.055 −1.076 271.165 −2.609 −0.406 271.165 −3.149 0.19236 271.165 −3.676 0.67431 271.165 −4.173 1.654 271.165 −4.640 2.325 271.165 −5.079 2.982 271.165 −5.491 3.625 271.165 −5.875 4.250 271.165 −6.232 4.858 271.165 −6.563 5.446 271.165 −6.868 6.015 271.165 −7.136 6.538 271.165 −7.367 7.013 271.165 −7.564 7.440 271.165 −7.739 7.844 271.165 −7.883 8.197 271.165 −7.983 8.473 271.165 −8.050 8.698 271.165 −8.088 8.871 271.165 −8.100 9.003 271.165 −8.093 9.077 271.165 −8.077 9.121 271.165 −8.062 9.140 271.165 −8.053 9.147 271.165 −8.158 8.724 275.374 −8.153 8.727 275.374 −8.141 8.729 275.374 −8.118 8.727 275.374 −8.075 8.708 275.374 −8.017 8.665 275.374 −7.923 8.575 275.374 −7.809 8.444 275.374 −7.666 8.263 275.374 −7.493 8.033 275.374 −7.272 7.729 275.374 −7.020 7.378 275.374 −6.749 7.003 275.374 −6.446 6.582 275.374 −6.108 6.114 275.374 −5.734 5.600 275.374 −5.340 5.066 275.374 −4.927 4.510 275.374 −4.493 3.933 275.374 −4.038 3.337 275.374 −3.562 2.720 275.374 −3.064 2.084 275.374 −2.544 1.428 275.374 −2.001 0.52292 275.374 −1.456 0.081 275.374 −0.907 −0.589 275.374 −0.355 −1.256 275.374 0.13889 −1.921 275.374 0.52639 −2.583 275.374 1.319 −3.243 275.374 1.882 −3.900 275.374 2.448 −4.555 275.374 3.018 −5.207 275.374 3.590 −5.857 275.374 4.166 −6.503 275.374 4.727 −7.125 275.374 5.272 −7.721 275.374 5.800 −8.294 275.374 6.313 −8.842 275.374 6.809 −9.366 275.374 7.288 −9.866 275.374 7.750 −10.343 275.374 8.175 −10.775 275.374 8.562 −11.163 275.374 8.911 −11.509 275.374 9.220 −11.812 275.374 9.490 −12.072 275.374 9.721 −12.291 275.374 9.919 −12.476 275.374 10.086 −12.631 275.374 10.224 −12.758 275.374 10.335 −12.859 275.374 10.414 −12.942 275.374 10.444 −13.025 275.374 10.442 −13.098 275.374 10.422 −13.153 275.374 10.397 −13.190 275.374 10.365 −13.220 275.374 10.313 −13.249 275.374 10.241 −13.263 275.374 10.155 −13.244 275.374 10.061 −13.175 275.374 9.943 −13.078 275.374 9.797 −12.956 275.374 9.619 −12.808 275.374 9.407 −12.632 275.374 9.158 −12.427 275.374 8.864 −12.185 275.374 8.525 −11.906 275.374 8.140 −11.589 275.374 7.712 −11.234 275.374 7.241 −10.838 275.374 6.727 −10.402 275.374 6.194 −9.944 275.374 5.643 −9.462 275.374 5.075 −8.956 275.374 4.490 −8.426 275.374 3.890 −7.870 275.374 3.276 −7.289 275.374 2.648 −6.680 275.374 2.028 −6.064 275.374 1.417 −5.440 275.374 0.56528 −4.808 275.374 0.15417 −4.168 275.374 −0.362 −3.518 275.374 −0.935 −2.860 275.374 −1.499 −2.194 275.374 −2.054 −1.518 275.374 −2.597 −0.833 275.374 −3.129 −0.138 275.374 −3.651 0.39444 275.374 −4.144 1.259 275.374 −4.610 1.936 275.374 −5.050 2.597 275.374 −5.462 3.240 275.374 −5.849 3.864 275.374 −6.211 4.470 275.374 −6.548 5.056 275.374 −6.862 5.621 275.374 −7.139 6.140 275.374 −7.380 6.610 275.374 −7.588 7.032 275.374 −7.776 7.431 275.374 −7.932 7.780 275.374 −8.044 8.052 275.374 −8.122 8.273 275.374 −8.170 8.443 275.374 −8.192 8.574 275.374 −8.194 8.647 275.374 −8.184 8.693 275.374 −8.172 8.713 275.374 −8.163 8.721 275.374 −8.263 8.345 279.583 −8.257 8.348 279.583 −8.245 8.350 279.583 −8.222 8.348 279.583 −8.178 8.329 279.583 −8.117 8.286 279.583 −8.021 8.194 279.583 −7.904 8.061 279.583 −7.757 7.876 279.583 −7.579 7.639 279.583 −7.353 7.328 279.583 −7.095 6.968 279.583 −6.819 6.583 279.583 −6.510 6.150 279.583 −6.166 5.668 279.583 −5.787 5.139 279.583 −5.390 4.587 279.583 −4.973 4.013 279.583 −4.537 3.416 279.583 −4.080 2.797 279.583 −3.603 2.157 279.583 −3.104 1.497 279.583 −2.583 0.56597 279.583 −2.041 0.07847 279.583 −1.496 −0.587 279.583 −0.948 −1.285 279.583 −0.399 −1.982 279.583 0.10625 −2.677 279.583 0.49236 −3.369 279.583 1.266 −4.059 279.583 1.826 −4.747 279.583 2.389 −5.433 279.583 2.954 −6.117 279.583 3.524 −6.797 279.583 4.097 −7.474 279.583 4.655 −8.125 279.583 5.198 −8.751 279.583 5.724 −9.351 279.583 6.235 −9.926 279.583 6.729 −10.476 279.583 7.207 −11.001 279.583 7.668 −11.501 279.583 8.092 −11.955 279.583 8.478 −12.363 279.583 8.826 −12.727 279.583 9.134 −13.045 279.583 9.404 −13.319 279.583 9.634 −13.549 279.583 9.832 −13.744 279.583 10.000 −13.907 279.583 10.138 −14.041 279.583 10.249 −14.147 279.583 10.330 −14.233 279.583 10.360 −14.317 279.583 10.358 −14.392 279.583 10.336 −14.448 279.583 10.310 −14.486 279.583 10.277 −14.516 279.583 10.223 −14.544 279.583 10.149 −14.555 279.583 10.061 −14.531 279.583 9.967 −14.457 279.583 9.850 −14.354 279.583 9.703 −14.226 279.583 9.524 −14.071 279.583 9.311 −13.886 279.583 9.061 −13.671 279.583 8.765 −13.417 279.583 8.424 −13.123 279.583 8.038 −12.790 279.583 7.608 −12.417 279.583 7.135 −12.001 279.583 6.618 −11.544 279.583 6.083 −11.063 279.583 5.529 −10.558 279.583 4.959 −10.028 279.583 4.372 −9.473 279.583 3.771 −8.891 279.583 3.155 −8.282 279.583 2.526 −7.644 279.583 1.906 −6.998 279.583 1.295 −6.344 279.583 0.48125 −5.682 279.583 0.07014 −5.011 279.583 −0.481 −4.331 279.583 −1.053 −3.642 279.583 −1.615 −2.944 279.583 −2.168 −2.238 279.583 −2.709 −1.521 279.583 −3.241 −0.796 279.583 −3.761 −0.060 279.583 −4.254 0.45694 279.583 −4.718 1.360 279.583 −5.155 2.043 279.583 −5.565 2.708 279.583 −5.950 3.353 279.583 −6.311 3.978 279.583 −6.648 4.581 279.583 −6.962 5.163 279.583 −7.240 5.696 279.583 −7.483 6.179 279.583 −7.691 6.612 279.583 −7.880 7.021 279.583 −8.038 7.379 279.583 −8.151 7.657 279.583 −8.231 7.884 279.583 −8.278 8.058 279.583 −8.300 8.192 279.583 −8.300 8.267 279.583 −8.289 8.313 279.583 −8.277 8.334 279.583 −8.268 8.342 279.583 −8.384 8.472 283.792 −8.378 8.475 283.792 −8.366 8.477 283.792 −8.341 8.475 283.792 −8.296 8.454 283.792 −8.235 8.408 283.792 −8.138 8.310 283.792 −8.020 8.170 283.792 −7.872 7.976 283.792 −7.692 7.728 283.792 −7.465 7.402 283.792 −7.205 7.025 283.792 −6.929 6.622 283.792 −6.619 6.167 283.792 −6.276 5.661 283.792 −5.898 5.105 283.792 −5.502 4.525 283.792 −5.087 3.920 283.792 −4.653 3.292 283.792 −4.198 2.640 283.792 −3.722 1.966 283.792 −3.225 1.269 283.792 −2.707 0.38194 283.792 −2.167 −0.191 283.792 −1.625 −0.929 283.792 −1.079 −1.666 283.792 −0.530 −2.400 283.792 0.022 −3.132 283.792 0.40069 −3.862 283.792 1.136 −4.588 283.792 1.697 −5.313 283.792 2.261 −6.036 283.792 2.829 −6.756 283.792 3.399 −7.473 283.792 3.974 −8.188 283.792 4.532 −8.876 283.792 5.075 −9.537 283.792 5.602 −10.172 283.792 6.113 −10.781 283.792 6.607 −11.363 283.792 7.085 −11.920 283.792 7.546 −12.450 283.792 7.970 −12.932 283.792 8.356 −13.365 283.792 8.705 −13.751 283.792 9.014 −14.089 283.792 9.285 −14.380 283.792 9.516 −14.624 283.792 9.715 −14.831 283.792 9.884 −15.004 283.792 10.023 −15.145 283.792 10.135 −15.258 283.792 10.217 −15.348 283.792 10.249 −15.434 283.792 10.245 −15.510 283.792 10.223 −15.567 283.792 10.196 −15.605 283.792 10.160 −15.635 283.792 10.104 −15.662 283.792 10.027 −15.670 283.792 9.938 −15.641 283.792 9.843 −15.561 283.792 9.724 −15.453 283.792 9.574 −15.319 283.792 9.391 −15.155 283.792 9.174 −14.961 283.792 8.919 −14.734 283.792 8.617 −14.467 283.792 8.269 −14.158 283.792 7.876 −13.807 283.792 7.438 −13.412 283.792 6.957 −12.974 283.792 6.433 −12.490 283.792 5.891 −11.981 283.792 5.331 −11.445 283.792 4.755 −10.883 283.792 4.164 −10.293 283.792 3.558 −9.675 283.792 2.940 −9.028 283.792 2.310 −8.351 283.792 1.689 −7.666 283.792 1.079 −6.972 283.792 0.33264 −6.270 283.792 −0.110 −5.558 283.792 −0.689 −4.837 283.792 −1.256 −4.108 283.792 −1.813 −3.369 283.792 −2.359 −2.621 283.792 −2.893 −1.864 283.792 −3.417 −1.098 283.792 −3.931 −0.324 283.792 −4.416 0.30139 283.792 −4.875 1.173 283.792 −5.307 1.891 283.792 −5.713 2.589 283.792 −6.093 3.265 283.792 −6.450 3.920 283.792 −6.784 4.551 283.792 −7.094 5.160 283.792 −7.370 5.716 283.792 −7.611 6.221 283.792 −7.818 6.672 283.792 −8.006 7.099 283.792 −8.163 7.471 283.792 −8.276 7.760 283.792 −8.355 7.995 283.792 −8.402 8.176 283.792 −8.423 8.314 283.792 −8.423 8.391 283.792 −8.411 8.440 283.792 −8.398 8.461 283.792 −8.389 8.469 283.792 −8.429 8.614 285.054 −8.423 8.617 285.054 −8.411 8.620 285.054 −8.386 8.617 285.054 −8.340 8.597 285.054 −8.278 8.550 285.054 −8.179 8.452 285.054 −8.061 8.309 285.054 −7.911 8.113 285.054 −7.730 7.862 285.054 −7.502 7.532 285.054 −7.241 7.148 285.054 −6.964 6.739 285.054 −6.654 6.277 285.054 −6.311 5.764 285.054 −5.932 5.199 285.054 −5.535 4.609 285.054 −5.120 3.995 285.054 −4.685 3.357 285.054 −4.230 2.695 285.054 −3.755 2.009 285.054 −3.259 1.300 285.054 −2.741 0.39514 285.054 −2.202 −0.185 285.054 −1.660 −0.937 285.054 −1.113 −1.686 285.054 −0.565 −2.433 285.054 −0.013 −3.177 285.054 0.37639 −3.920 285.054 1.100 −4.660 285.054 1.661 −5.398 285.054 2.224 −6.135 285.054 2.789 −6.869 285.054 3.358 −7.601 285.054 3.931 −8.330 285.054 4.487 −9.032 285.054 5.028 −9.707 285.054 5.553 −10.356 285.054 6.062 −10.977 285.054 6.555 −11.572 285.054 7.031 −12.141 285.054 7.490 −12.683 285.054 7.914 −13.175 285.054 8.299 −13.617 285.054 8.647 −14.011 285.054 8.956 −14.356 285.054 9.227 −14.653 285.054 9.458 −14.902 285.054 9.658 −15.113 285.054 9.827 −15.289 285.054 9.966 −15.434 285.054 10.079 −15.549 285.054 10.162 −15.639 285.054 10.196 −15.727 285.054 10.192 −15.805 285.054 10.170 −15.863 285.054 10.142 −15.901 285.054 10.106 −15.932 285.054 10.048 −15.959 285.054 9.970 −15.966 285.054 9.881 −15.935 285.054 9.786 −15.853 285.054 9.664 −15.743 285.054 9.513 −15.607 285.054 9.328 −15.441 285.054 9.109 −15.243 285.054 8.851 −15.013 285.054 8.546 −14.742 285.054 8.194 −14.429 285.054 7.796 −14.072 285.054 7.353 −13.672 285.054 6.866 −13.227 285.054 6.336 −12.736 285.054 5.788 −12.219 285.054 5.222 −11.675 285.054 4.640 −11.104 285.054 4.043 −10.504 285.054 3.433 −9.876 285.054 2.811 −9.217 285.054 2.177 −8.528 285.054 1.554 −7.831 285.054 0.65417 −7.124 285.054 0.23681 −6.409 285.054 −0.249 −5.684 285.054 −0.826 −4.950 285.054 −1.392 −4.208 285.054 −1.948 −3.456 285.054 −2.491 −2.695 285.054 −3.023 −1.924 285.054 −3.543 −1.144 285.054 −4.051 −0.355 285.054 −4.532 0.28889 285.054 −4.986 1.170 285.054 −5.413 1.903 285.054 −5.815 2.616 285.054 −6.191 3.306 285.054 −6.544 3.974 285.054 −6.873 4.618 285.054 −7.179 5.239 285.054 −7.450 5.807 285.054 −7.686 6.321 285.054 −7.890 6.782 285.054 −8.073 7.216 285.054 −8.226 7.596 285.054 −8.335 7.891 285.054 −8.411 8.131 285.054 −8.455 8.314 285.054 −8.473 8.455 285.054 −8.470 8.533 285.054 −8.457 8.582 285.054 −8.443 8.603 285.054 −8.434 8.611 285.054 −8.544 9.086 288.000 −8.538 9.088 288.000 −8.525 9.091 288.000 −8.500 9.088 288.000 −8.454 9.066 288.000 −8.391 9.018 288.000 −8.291 8.915 288.000 −8.172 8.768 288.000 −8.021 8.564 288.000 −7.840 8.305 288.000 −7.612 7.962 288.000 −7.354 7.564 288.000 −7.079 7.138 288.000 −6.772 6.659 288.000 −6.432 6.125 288.000 −6.057 5.538 288.000 −5.664 4.925 288.000 −5.253 4.286 288.000 −4.824 3.622 288.000 −4.374 2.933 288.000 −3.905 2.219 288.000 −3.415 1.480 288.000 −2.905 0.49792 288.000 −2.373 −0.069 288.000 −1.838 −0.853 288.000 −1.300 −1.635 288.000 −0.758 −2.415 288.000 −0.214 −3.194 288.000 0.23125 −3.970 288.000 0.61319 −4.743 288.000 1.435 −5.516 288.000 1.990 −6.286 288.000 2.547 −7.055 288.000 3.107 −7.822 288.000 3.671 −8.585 288.000 4.220 −9.321 288.000 4.754 −10.028 288.000 5.273 −10.707 288.000 5.776 −11.358 288.000 6.263 −11.982 288.000 6.735 −12.577 288.000 7.190 −13.145 288.000 7.611 −13.660 288.000 7.994 −14.123 288.000 8.341 −14.535 288.000 8.649 −14.896 288.000 8.919 −15.206 288.000 9.151 −15.466 288.000 9.351 −15.686 288.000 9.521 −15.869 288.000 9.662 −16.020 288.000 9.775 −16.139 288.000 9.860 −16.232 288.000 9.896 −16.321 288.000 9.893 −16.401 288.000 9.869 −16.461 288.000 9.840 −16.500 288.000 9.803 −16.531 288.000 9.744 −16.558 288.000 9.663 −16.563 288.000 9.573 −16.528 288.000 9.477 −16.442 288.000 9.354 −16.328 288.000 9.199 −16.186 288.000 9.011 −16.014 288.000 8.788 −15.810 288.000 8.525 −15.571 288.000 8.215 −15.289 288.000 7.857 −14.963 288.000 7.453 −14.593 288.000 7.003 −14.177 288.000 6.510 −13.713 288.000 5.973 −13.202 288.000 5.417 −12.662 288.000 4.845 −12.094 288.000 4.258 −11.498 288.000 3.657 −10.872 288.000 3.043 −10.215 288.000 2.418 −9.527 288.000 1.784 −8.807 288.000 1.161 −8.078 288.000 0.38194 −7.339 288.000 −0.048 −6.591 288.000 −0.632 −5.833 288.000 −1.203 −5.065 288.000 −1.762 −4.287 288.000 −2.309 −3.501 288.000 −2.843 −2.705 288.000 −3.364 −1.899 288.000 −3.873 −1.084 288.000 −4.370 −0.260 288.000 −4.838 0.37847 288.000 −5.280 1.331 288.000 −5.695 2.096 288.000 −6.084 2.840 288.000 −6.448 3.560 288.000 −6.788 4.257 288.000 −7.103 4.929 288.000 −7.396 5.576 288.000 −7.654 6.168 288.000 −7.877 6.705 288.000 −8.068 7.184 288.000 −8.240 7.637 288.000 −8.380 8.033 288.000 −8.480 8.340 288.000 −8.547 8.589 288.000 −8.585 8.779 288.000 −8.597 8.924 288.000 −8.591 9.004 288.000 −8.575 9.053 288.000 −8.559 9.074 288.000 −8.549 9.082 288.000

At the same time, each blade 10 therefore has an aerodynamic profile which allows a high conversion efficiency and a high useful life to be maintained.

Furthermore, the aerodynamic profile of the blade 10 according to the invention is obtained with the values of Table I by piling up the series of closed curves and grouping them so as to obtain a continuous aerodynamic profile.

In order to take into account the dimensional variability of each blade 10, the profile of each blade 10 can have a tolerance of ±2 mm in a normal direction with respect to the profile of the blade 10 itself.

The profile of each blade 10 can also comprise a coating, applied subsequently and which varies the profile itself.

Said antiwear coating preferably has a thickness defined in a normal direction at each surface of the blade 10 and ranging from 0 to 0.5 mm.

It is evident, moreover, that the values of the coordinates of Table I can be multiplied or divided by a corrective constant to obtain a profile in a greater or smaller scale, maintaining the same form.

According to another aspect of the present invention, a rotor of a ninth phase of a compressor is provided, which comprises a series of blades 10 of the type described above, each of which having a shaped aerodynamic profile, which are fixed to an outer surface of said rotor so as to be uniformly distanced thereon, and also oriented so as to confer a high efficiency to the compressor in which said rotor is preferably inserted.

According to another aspect of the present invention, a compressor is provided, comprising a rotor of the type described above.

It can thus be seen that a blade of a rotor of a ninth phase of a compressor according to the present invention achieves the objectives specified above.

The rotor blade of a ninth phase of a compressor of the present invention thus conceived, can undergo numerous modifications and variants, all included in the same inventive concept.

Furthermore, in practice, the materials used, as also the dimensions and components, can vary according to technical requirements. 

1. A blade (10) of a rotor of a ninth phase of a compressor, which can be defined by coordinates of a discreet combination of points, in a Cartesian reference system (X, Y. Z), wherein the axis (Z) is a radial axis intersecting the central axis of the compressor, said blade (10) having a profile which can be identified by means of a series of closed intersection curves between the profile itself and planes (X, Y) lying at distances (Z) from the central axis, said blade (10) being characterized in that it comprises a thickening (30), substantially parallel to a base portion (12) of the blade (10) itself, fixable to said rotor, said thickening (30) being substantially situated halfway up the blade (10) and being suitable for shifting the natural resonance frequencies of the blade (10) itself outside a functioning frequency range of said rotor.
 2. The blade (10) according to claim 1, characterized in that it comprises a further thickening, substantially parallel to said base portion (12) and situated in particular close to a free end (14).
 3. The blade (10) according to claim 1, characterized in that it comprises a profile which is identified by a first substantially concave surface (3), which is pressurized, and a second substantially convex surface (5) which is in depression and which is opposite to the first, said two surfaces (3, 5) being continuous and joined to each other to form the profile of said blade
 10. 4. The blade (10) according to claim 3, characterized in that each closed curve has a maximum thickness determined by the maximum distance between said first surface (3) and said second surface (5), said maximum thickness of each closed curve, along the height of the blade 10 in the direction of a free end (14) of the blade (10), first having a decreasing and then an increasing trend, followed again by a decreasing and finally increasing trend, with a discontinuity point of the slope.
 5. The blade (10) according to claim 4, characterized in that along the height of the blade (10) in the direction of its free end (14), said maximum thickness has a trend according to the following equations, wherein h represents the height of the blade (10), expressed as a percentage of the total height of the blade (10), and wherein Tmax is the maximum adimensionalized thickness relating to the closed curve corresponding to the height: Tmax=−34.522*h ⁴+36.4*h ³−8.4113*h ²−0.7259*h+0.9961 for height values ranging from 0 to 45%; Tmax=−1.3509*h+1.4459 for a height ranging from 45% to 58%; Tmax=0.2074*h+0.5443 for a height ranging from 58% to 86%; Tmax=0.9058*h−0.0518 for a height ranging from 86% to 100%.
 6. The blade (10) according to claim 5, characterized in that said closed curves are defined according to Table I, whose values, expressed in millimeters, refer to a profile at room temperature.
 7. The blade (10) according to claim 6, characterized in that the profile of each blade (10) has a tolerance of ±2 mm in a normal direction with respect to the profile of the blade 10 itself.
 8. The blade (10) according to claim 7, characterized in that the profile of each blade (10) comprises an antiwear coating.
 9. The blade (10) according to claim 8, characterized in that said coating has a thickness ranging from 0 to 0.5 mm.
 10. A rotor of a ninth phase of a compressor, characterized in that it comprises a series of blades (10) according to claim
 1. 11. The rotor according to claim 10, characterized in that said series of blades (10) is constrained to an outer surface of said rotor and said series of blades (10) is also uniformly distributed thereon in order to maximize the efficiency of the rotor itself.
 12. A compressor characterized in that it comprises a rotor according to claim
 10. 